## TSTP Solution File: SYN721+1 by E---3.0

View Problem - Process Solution

```%------------------------------------------------------------------------------
% File     : E---3.0
% Problem  : SYN721+1 : TPTP v8.1.0. Released v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n020.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Sep 29 21:43:56 EDT 2022

% Result   : Theorem 0.20s 0.47s
% Output   : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   15 (   5 unt;   4 typ;   0 def)
%            Number of atoms       :   32 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   31 (  10   ~;   6   |;   9   &)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    4 (   2   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   25 (   4 sgn  14   !;   4   ?;   0   :)

%------------------------------------------------------------------------------
tff(decl_22,type,
a: \$i ).

tff(decl_23,type,
b: \$i ).

tff(decl_24,type,
r: ( \$i * \$i ) > \$o ).

tff(decl_25,type,
q: ( \$i * \$i ) > \$o ).

fof(lx1,conjecture,
( ( r(a,b)
& ! [X1] :
( ? [X2] : r(X1,X2)
=> q(X1,X1) )
& ! [X3,X4] :
( q(X3,X4)
=> ! [X5] : r(X5,X4) ) )
=> ? [X6] :
( r(b,X6)
& q(X6,a) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lx1) ).

fof(c_0_1,negated_conjecture,
~ ( ( r(a,b)
& ! [X1] :
( ? [X2] : r(X1,X2)
=> q(X1,X1) )
& ! [X3,X4] :
( q(X3,X4)
=> ! [X5] : r(X5,X4) ) )
=> ? [X6] :
( r(b,X6)
& q(X6,a) ) ),
inference(assume_negation,[status(cth)],[lx1]) ).

fof(c_0_2,negated_conjecture,
! [X7,X8,X9,X10,X11,X12] :
( r(a,b)
& ( ~ r(X7,X8)
| q(X7,X7) )
& ( ~ q(X9,X10)
| r(X11,X10) )
& ( ~ r(b,X12)
| ~ q(X12,a) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])]) ).

cnf(c_0_3,negated_conjecture,
( q(X1,X1)
| ~ r(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_4,negated_conjecture,
r(a,b),
inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_5,negated_conjecture,
( ~ r(b,X1)
| ~ q(X1,a) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_6,negated_conjecture,
q(a,a),
inference(spm,[status(thm)],[c_0_3,c_0_4]) ).

cnf(c_0_7,negated_conjecture,
( r(X3,X2)
| ~ q(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_2]) ).

cnf(c_0_8,negated_conjecture,
~ r(b,a),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).

cnf(c_0_9,negated_conjecture,
r(X1,a),
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).

cnf(c_0_10,negated_conjecture,
\$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_9])]),
[proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SYN721+1 : TPTP v8.1.0. Released v2.5.0.
% 0.11/0.13  % Command    : run_E %s %d THM
% 0.13/0.34  % Computer : n020.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon Sep  5 06:47:13 EDT 2022
% 0.13/0.34  % CPUTime    :
% 0.20/0.47  Running first-order on 8 cores theorem proving
% 0.20/0.47  Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.47  # Version: 3.0pre003
% 0.20/0.47  # Preprocessing class: FSSSSMSSSSSNFFN.
% 0.20/0.47  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.47  # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.20/0.47  # Starting new_bool_3 with 300s (1) cores
% 0.20/0.47  # Starting new_bool_1 with 300s (1) cores
% 0.20/0.47  # Starting sh5l with 300s (1) cores
% 0.20/0.47  # new_bool_3 with pid 3119 completed with status 0
% 0.20/0.47  # Result found by new_bool_3
% 0.20/0.47  # Preprocessing class: FSSSSMSSSSSNFFN.
% 0.20/0.47  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.47  # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.20/0.47  # Starting new_bool_3 with 300s (1) cores
% 0.20/0.47  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.47  # ...ProofStateSinE()=1/1
% 0.20/0.47  # Search class: FHHNF-FFSF00-SFFFFFNN
% 0.20/0.47  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.47  # Starting SAT001_MinMin_p005000_rr_RG with 181s (1) cores
% 0.20/0.47  # SAT001_MinMin_p005000_rr_RG with pid 3124 completed with status 0
% 0.20/0.47  # Result found by SAT001_MinMin_p005000_rr_RG
% 0.20/0.47  # Preprocessing class: FSSSSMSSSSSNFFN.
% 0.20/0.47  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.47  # Starting G-E--_302_C18_F1_URBAN_RG_S04BN with 1500s (5) cores
% 0.20/0.47  # Starting new_bool_3 with 300s (1) cores
% 0.20/0.47  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.20/0.47  # ...ProofStateSinE()=1/1
% 0.20/0.47  # Search class: FHHNF-FFSF00-SFFFFFNN
% 0.20/0.47  # Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.20/0.47  # Starting SAT001_MinMin_p005000_rr_RG with 181s (1) cores
% 0.20/0.47  # Preprocessing time       : 0.001 s
% 0.20/0.47  # Presaturation interreduction done
% 0.20/0.47
% 0.20/0.47  # Proof found!
% 0.20/0.47  # SZS status Theorem
% 0.20/0.47  # SZS output start CNFRefutation
% See solution above
% 0.20/0.47  # Parsed axioms                        : 1
% 0.20/0.47  # Removed by relevancy pruning/SinE    : 0
% 0.20/0.47  # Initial clauses                      : 4
% 0.20/0.47  # Removed in clause preprocessing      : 0
% 0.20/0.47  # Initial clauses in saturation        : 4
% 0.20/0.47  # Processed clauses                    : 11
% 0.20/0.47  # ...of these trivial                  : 0
% 0.20/0.47  # ...subsumed                          : 0
% 0.20/0.47  # ...remaining for further processing  : 11
% 0.20/0.47  # Other redundant clauses eliminated   : 0
% 0.20/0.47  # Clauses deleted for lack of memory   : 0
% 0.20/0.47  # Backward-subsumed                    : 0
% 0.20/0.47  # Backward-rewritten                   : 1
% 0.20/0.47  # Generated clauses                    : 4
% 0.20/0.47  # ...of the previous two non-redundant : 3
% 0.20/0.47  # ...aggressively subsumed             : 0
% 0.20/0.47  # Contextual simplify-reflections      : 0
% 0.20/0.47  # Paramodulations                      : 4
% 0.20/0.47  # Factorizations                       : 0
% 0.20/0.47  # NegExts                              : 0
% 0.20/0.47  # Equation resolutions                 : 0
% 0.20/0.47  # Propositional unsat checks           : 0
% 0.20/0.47  #    Propositional check models        : 0
% 0.20/0.47  #    Propositional check unsatisfiable : 0
% 0.20/0.47  #    Propositional clauses             : 0
% 0.20/0.47  #    Propositional clauses after purity: 0
% 0.20/0.47  #    Propositional unsat core size     : 0
% 0.20/0.47  #    Propositional preprocessing time  : 0.000
% 0.20/0.47  #    Propositional encoding time       : 0.000
% 0.20/0.47  #    Propositional solver time         : 0.000
% 0.20/0.47  #    Success case prop preproc time    : 0.000
% 0.20/0.47  #    Success case prop encoding time   : 0.000
% 0.20/0.47  #    Success case prop solver time     : 0.000
% 0.20/0.47  # Current number of processed clauses  : 6
% 0.20/0.47  #    Positive orientable unit clauses  : 3
% 0.20/0.47  #    Positive unorientable unit clauses: 0
% 0.20/0.47  #    Negative unit clauses             : 0
% 0.20/0.47  #    Non-unit-clauses                  : 3
% 0.20/0.47  # Current number of unprocessed clauses: 0
% 0.20/0.47  # ...number of literals in the above   : 0
% 0.20/0.47  # Current number of archived formulas  : 0
% 0.20/0.47  # Current number of archived clauses   : 5
% 0.20/0.47  # Clause-clause subsumption calls (NU) : 0
% 0.20/0.47  # Rec. Clause-clause subsumption calls : 0
% 0.20/0.47  # Non-unit clause-clause subsumptions  : 0
% 0.20/0.47  # Unit Clause-clause subsumption calls : 1
% 0.20/0.47  # Rewrite failures with RHS unbound    : 0
% 0.20/0.47  # BW rewrite match attempts            : 1
% 0.20/0.47  # BW rewrite match successes           : 1
% 0.20/0.47  # Condensation attempts                : 0
% 0.20/0.47  # Condensation successes               : 0
% 0.20/0.47  # Termbank termtop insertions          : 343
% 0.20/0.47
% 0.20/0.47  # -------------------------------------------------
% 0.20/0.47  # User time                : 0.003 s
% 0.20/0.47  # System time              : 0.001 s
% 0.20/0.47  # Total time               : 0.004 s
% 0.20/0.47  # Maximum resident set size: 1580 pages
% 0.20/0.47
% 0.20/0.47  # -------------------------------------------------
% 0.20/0.47  # User time                : 0.005 s
% 0.20/0.47  # System time              : 0.002 s
% 0.20/0.47  # Total time               : 0.006 s
% 0.20/0.47  # Maximum resident set size: 1696 pages
%------------------------------------------------------------------------------
```